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Saturation, HSaturation
Syntax
Saturation(I:IDEAL,J:IDEAL):IDEAL
HSaturation(I:IDEAL,J:IDEAL):IDEAL
Summary
saturation of ideals
Description
These functions return the saturation of I with respect to J: the
ideal of polynomials F such that FG is in I for all G in J^d for some
positive integer d.
The function
HSaturation
calculates the saturation using a
Hilbert-driven algorithm. It differs from
Saturation
only when the
input is inhomogeneous, in which case,
HSaturation
may be faster.
The coefficient ring must be a field.
example
Use R ::= Q[xyz];
I := Ideal(x-z,y-2z);
J := Ideal(x-2z,y-z);
K := Intersection(I,J); -- ideal of two points in the
-- projective plane
L := Intersection(K,Ideal(x,y,z)^3); -- add an irrelevant component
Hilbert(R/L);
H(0) = 1
H(1) = 3
H(2) = 6
H(t) = 2 for t >= 3
-------------------------------
Saturation(L,Ideal(x,y,z)) = K; -- saturating gets rid of the
-- irrelevant component
TRUE
-------------------------------
See Also